Massachusetts labor department officials told a state Senate committee Monday that it might take until February to completely fix problems plaguing the new online system for filing unemployment benefits.

But even with the possibility that unemployed workers could face months more of difficulties and delays in getting benefits, officials from the Labor Department and contractor, Deloitte Consulting of New York, testified before the Senate Committee on Post Audit that the rollout of the computer system was largely a success.

“I am happy with the launch,” said Joanne F. Goldstein,
secretary of Labor and Workforce Development, noting that she would have liked some aspects to have gone better.

Mark Price, a Deloitte principal in charge of the firm’s Massachusetts business, acknowledged that software has faced challenges during the rollout, but insisted, “We have a successful working system today.’’

The testimony painted a starkly different vision of the state’s new $46 million unemployment system than the one offered by hundreds of job seekers who have called and e-mailed legislators to say the system has failed them. Many who were receiving benefits experienced problems only after the July 1 rollout, and when they called the state for help, spent hours on hold, often only to be disconnected.

State Senator Cynthia Stone Creem, the Newton Democrat who is chairwoman of the committee, expressed disbelief at Deloitte’s view of the system. She said she would schedule another hearing to question Deloitte officials further.

“As I sit here today, I haven’t heard anything you think Deloitte might have done differently,’’ Creem told executives of the firm called to testify. “I’m just at a loss.”

Deloitte has come under fire in Massachusetts and other states where it has built computer systems to handle payrolls, court records, and unemployment benefits. The glitch-ridden Massachusetts system for managing unemployment claims was delivered two years late and $6 million over budget.

Deloitte was fired from a separate $114 million modernization project for the Department of Revenue in August. State officials said a test run of the software last year revealed 1,000 glitches and they eventually terminated the contract.

The state also recently awarded another contract to Deloitte worth $76.8 million to modernize the Registry of Motor Vehicles customer system.

Price defended the firm’s work for the Department of Revenue, even though the state paid $54 million on the project, never used the system, and terminated the contract with the consultant early. “We built a workable solution for the Commonwealth,” Price said of the system, noting that Deloitte fixed problems after the test run.

Creem asked Price whether Deloitte had faced trouble rolling out unemployment benefits systems in other states, problems that have been extensively reported in California and Florida.

Price said: “Clients will tell you the systems are working well.”

Creem asked him if media accounts were wrong, to which Price responded: “From my perspective, the systems are working well.”

In Massachusetts, Price said, there have been 100 to 300 claims issues related to the conversion to the new system “in any given week.”

Price, however, said he was not asked specifically to reveal the total number of people affected by the problems or whether there was a backlog in paying claims.

The state has hired an additional 100 call center employees to deal with issues and complaints, paying state employees overtime to handle the volume of calls. Michelle Amante, director of the Division of Unemployment, told the Senate committee that the average wait time is still 45 minutes — roughly double what it was before the launch of the system — and sometimes lasts more than a hour.

Amante, a former Deloitte manager, said the state has until the end of a warranty period, which expires this week, to identify problems for the consultant to fix. When asked by Creem when 80 Deloitte employees would “be gone” from the project, Amante said, “My guess, it will probably be February.”

Goldstein, the state labor secretary, testified that the goal is “make sure the process worked as efficiently as possible.”

Creem asked why the department agreed to pay millions of dollars more to the contractor after Deloitte missed a 2011 deadline to deliver the work. Goldstein said it was partly because the state was delayed in providing information and other support to Deloitte because of the surge in claims during the last recession.

The priority was to pay claims and keep “the old system working,” Goldstein said.

Creem also grilled Department of Revenue Commissioner Amy Pitter about the project, noting that the state spent millions of dollars before firing Deloitte.

Creem questioned how it was that Deloitte could make millions on a project “that delivered no value for Massachusetts.”

Pitter, who inherited the project after she became commissioner in 2011, said the department was able to salvage some of Deloitte’s work.

Navjeet Bal, the former Revenue Department commissioner who now works in private practice with the law firm Nixon Peabody, testified that she hired outside lawyers from Bingham McCutchen LLP to help negotiate the contract when she was commissioner. She left the Revenue Department about two years ago, and said she was surprised to learn that the project failed at significant expense to taxpayers.

“We put an A team of people together to manage this project,” she said.